Problem: Simplify the following expression: $ a = \dfrac{-8}{3} + \dfrac{-6n + 7}{6n} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6n}{6n}$ $ \dfrac{-8}{3} \times \dfrac{6n}{6n} = \dfrac{-48n}{18n} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-6n + 7}{6n} \times \dfrac{3}{3} = \dfrac{-18n + 21}{18n} $ Therefore $ a = \dfrac{-48n}{18n} + \dfrac{-18n + 21}{18n} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-48n - 18n + 21}{18n} $ $a = \dfrac{-66n + 21}{18n}$ Simplify the expression by dividing the numerator and denominator by 3: $a = \dfrac{-22n + 7}{6n}$